Topic: Mathematicians/Statisticians of the fora
Anonymous A started this discussion 4 years ago #102,570
A calculator's random number generator (RNG) was programmed by a human, so how can it be truly random?
Anonymous B joined in and replied with this 4 years ago, 2 minutes later[^] [v] #1,158,883
It isn't. It's called pseudo-random. Input the same seed and you get the same string of random numbers.
If it were initialized by a truly random source, such as radioactive decay, as it goes in quantum mechanics, it would be truly random. But any calculator you have access to isn't doing that.
If it were initialized by a truly random source, such as radioactive decay, as it goes in quantum mechanics, it would be truly random. But any calculator you have access to isn't doing that.
Anonymous B double-posted this 4 years ago, 1 minute later, 4 minutes after the original post[^] [v] #1,158,885
Most computer programs initialize the seed by the clock and or thermal sensors. Which isn't technically random, but good enough for most uses.
Anonymous A (OP) replied with this 4 years ago, 19 seconds later, 4 minutes after the original post[^] [v] #1,158,886
Anonymous A (OP) double-posted this 4 years ago, 15 seconds later, 4 minutes after the original post[^] [v] #1,158,887
Anonymous A (OP) triple-posted this 4 years ago, 20 seconds later, 5 minutes after the original post[^] [v] #1,158,888
Ok, so if it is not truly random, then how can any statistics work done with it be considered truly valid?
Fake anon !ZkUt8arUCU joined in and replied with this 4 years ago, 26 seconds later, 5 minutes after the original post[^] [v] #1,158,889
If it takes a nonzero amount of time and materials to make one breadstick, how can Olive Garden truly offer unlimited breadsticks?
Anonymous A (OP) replied with this 4 years ago, 13 seconds later, 5 minutes after the original post[^] [v] #1,158,890
Anonymous D joined in and replied with this 4 years ago, 3 minutes later, 9 minutes after the original post[^] [v] #1,158,891
A calculator doesn't need a long repeatability period, 10,000 is going to be fine. An alternative is to measure the voltage on a wire, which should be zero but isn't.Probably the most sophisticated random number generator is a wall of lava lamps, take an uncompressed photo of the wall and you have a really random photo, repeatability of millions or trillions of years.
Anonymous B replied with this 4 years ago, 2 minutes later, 12 minutes after the original post[^] [v] #1,158,892
@1,158,888 (A)
Because the odds that you'd be consistently biasing the seed in the same way are not that high.
It's not typically a concern because most statistical tests already make assumptions (ex. assuming a "normal" [Gaussian] distribution) that are already far more tenuous than problems with the random number generator. Other assumptions like independence of sampling are technically never strictly satisfied either and virtually all statistical tests assume this at the most core level.
Hard-core cryptoanalyists can exploit problems in random number generators, but that's getting into NSA-level territory. A lot of work has been put into creating approaches for generating large amounts of high entropy bits just for the sake of seeding random number generators to avoid these problems. But that's more relevant for cryptography and not run of the mill statistical testing.
Because the odds that you'd be consistently biasing the seed in the same way are not that high.
It's not typically a concern because most statistical tests already make assumptions (ex. assuming a "normal" [Gaussian] distribution) that are already far more tenuous than problems with the random number generator. Other assumptions like independence of sampling are technically never strictly satisfied either and virtually all statistical tests assume this at the most core level.
Hard-core cryptoanalyists can exploit problems in random number generators, but that's getting into NSA-level territory. A lot of work has been put into creating approaches for generating large amounts of high entropy bits just for the sake of seeding random number generators to avoid these problems. But that's more relevant for cryptography and not run of the mill statistical testing.
Anonymous A (OP) replied with this 4 years ago, 1 minute later, 13 minutes after the original post[^] [v] #1,158,893
Thanks everyone.
Anonymous B replied with this 4 years ago, 1 second later, 13 minutes after the original post[^] [v] #1,158,894
@1,158,891 (D)
Yeah, chaotic systems are great sources of effectively, but not technically, random data.
Yeah, chaotic systems are great sources of effectively, but not technically, random data.
Anonymous D replied with this 4 years ago, 5 minutes later, 18 minutes after the original post[^] [v] #1,158,896
@previous (B)
> Yeah, chaotic systems are great sources of effectively, but not technically, random data.
For one lava lamp, sure but the lamp at the top left isn't going to have any effect on the lamp at the bottom right.
> Yeah, chaotic systems are great sources of effectively, but not technically, random data.
For one lava lamp, sure but the lamp at the top left isn't going to have any effect on the lamp at the bottom right.
Anonymous B replied with this 4 years ago, 5 minutes later, 24 minutes after the original post[^] [v] #1,158,897
@previous (D)
For all practical purposes, it will not.
If you, however, had an insanely accurate thermal sensor and an insanely accurate knowledge of the initial conditions, it would still be predictable though. Minor temperature variations will spread across the lamps unless they were somehow perfectly insulated from each other. You should, in principle, be able to predict their evolution, up until quantum effects become relevant. But that could take thousands of years at the scale of a lava lamp. Maybe? I don't know, that's my guess though.
For all practical purposes, it will not.
If you, however, had an insanely accurate thermal sensor and an insanely accurate knowledge of the initial conditions, it would still be predictable though. Minor temperature variations will spread across the lamps unless they were somehow perfectly insulated from each other. You should, in principle, be able to predict their evolution, up until quantum effects become relevant. But that could take thousands of years at the scale of a lava lamp. Maybe? I don't know, that's my guess though.
Anonymous B double-posted this 4 years ago, 10 minutes later, 35 minutes after the original post[^] [v] #1,158,899
Another problem with using classical sources of entropy (thermal sensors, weather patterns, lava lamps, ...) is that the outputs will be correlated in time. You won't see huge jumps in the values at close points in time and this makes it predictable. Even if you can't predict the whole sequence, you can start to approximate or narrow in where you think the seed values will be. And this can sometimes be exploited at least in regards to cryptoanalysis. It can be mitigated by not sampling so close in time, but that can create huge limits on your bandwidth of seed data which can be a problem in some cases.
Really the only way around this is to use a quantum source of entropy and people do in fact do this if they need military-grade encryption.
Really the only way around this is to use a quantum source of entropy and people do in fact do this if they need military-grade encryption.